A) Only one solution
B) Two solutions
C) Infinitely many solutions
D) No solution
Correct Answer: D
Solution :
Given equation is \[\sqrt{3}\sin x+\cos x=4\] which is of the form \[a\sin x+b\cos x=c\] with \[a=\sqrt{3},\,b=1,\,c=4\]. Here \[{{a}^{2}}+{{b}^{2}}=3+1=4<{{c}^{2}},\]therefore the given equation has no solution.
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